Please correct me if I'm wrong; Bootstrap is to get started quickly and to focus on functionality before you focus on form. Bootstrap allows you (as a developer) to quickly prototype without having to be bogged down by HTML/CSS details.
However, when you're ready for the next stage and want to implement your "real" design you don't have to shoehorn it into Bootstrap. You can just toss it out and use something else. And if you decide to keep using Bootstrap that's cool too...
Realize that Bootstrap is as much an HTML/JS framework as it is a CSS framework.
Looking at Bootstrap's examples it's pretty obvious how easy it is to make a Bootstrap-backed site look completely different.
Bootstrap was made to be used in parts, or as a whole, and has a lot of useful plugins (like their carousel).
Abandoning it outright because you don't like the way it looks just makes me think you're a back-end developer that doesn't want to put any effort into the UX/UI of the front-end.
However, when you're ready for the next stage and want to implement your "real" design you don't have to shoehorn it into Bootstrap. You can just toss it out and use something else. And if you decide to keep using Bootstrap that's cool too...